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Modifications of the Oettli-Prager Theorem with Application to the Eigenvalue Problem
 

Summary: 0
Modifications of the Oettli-Prager Theorem
with Application to the Eigenvalue Problem
G. Alefeld, V. Kreinovich, G. Mayer
Dedicated to Prof. Dr. Jiirgen Herzberger on the occasion 0/ his 60th birthday.
1 Introduction
In this paper we consider the eigenpair set
Ep := { (x,).) I Ax = ).x, x i=0, A E [AL A with property P}, (1)
where [A] is a given real n x n interval matrix (cf. Alefeld and Herzberger (1983),
e.g., for interval analysis) and P is some fixed property such as symmetry,
Toeplitz form, etc.. Before we study this set in greater detail we mention other
ones which are related to it: When dealing with systems of linear equations
Ax - b- , A E Jl{.nxn, bE Jl{.n (2)
(Jl{.n Xn set of real n x n matrices, ßRn set of real vectors with n components) there
sometimes occurs the problem of varying the input data A, b within certain
tolerances and looking for the set S of the resulting solutions x*. Examples of
this problem are Wilkinson's backward analysis when solving linear systems on
a computer (Wilkinson 1963) and an input-output model in economics which
is regulated by (2) with input parameters A, band output x (Maier 1985). In
the first example one solves (2) on a computer (assuming A to be nonsingular).

  

Source: Alefeld, Götz - Institut für Angewandte und Numerische Mathematik & Fakultät für Mathematik, Universität Karlsruhe

 

Collections: Mathematics